1. Field of the Invention
The present invention relates to an arrival direction estimation apparatus for estimating the arrival direction of electric waves and sound waves by using an antenna composed of a plurality of antenna elements.
2. Description of the Related Art
There have historically been a number of methods of estimating the arrival direction of, for example, electric waves and sound waves by using an array antenna composed of a plurality of antenna elements. The simplest method thereof is beam former method using the same principle as that of Fourier transform. As a method having a higher direction resolution, CAPON method, MUSIC (MUltiple SIgnal Classification) method based on null scanning and the like can be cited. These methods are disclosed in the following nonpatent document 1 and nonpatent document 2. A description will be hereinafter given of the arrival direction estimation taking existing MUSIC method as an example. The structure of an existing arrival direction estimation apparatus will be described by using FIG. 12. As shown in FIG. 12, signals received by a plurality of antenna elements 1201-1 to 1201-K are converted to complex digital signals by signal obtaining means 1202-1 to 1202-K of a complex digital signal obtaining means 1202. Next, a complex correlation matrix calculating means 1203 calculates a complex correlation matrix Rxx by performing correlation calculation among the plurality of antenna elements of the converted complex digital signals. When the antenna elements are arranged symmetrically, a real number correlation matrix Ryy is obtained by using unitary method. When the real number correlation matrix Ryy is used instead of Rxx, a subsequent eigen value decomposition calculation amount can be greatly reduced. The details of unitary method are disclosed in nonpatent document 1 and patent document 1.
The obtained complex correlation matrix Rxx (or real number correlation matrix Ryy) is inputted to a weight matrix calculating means 1204. In the case of MUSIC method, the correlation matrix is provided with eigen value decomposition, and a signal eigen space matrix Es=[e(1) . . . e(L)] (K*L matrix) and a noise eigen space matrix EN=[e(L+1) . . . e(K)] (K*(K−L) matrix) are calculated. L is the signal dimension number (the number of arrival waves). The obtained weight matrix w(in the case of MUSIC, w is a noise eigen space matrix EN) is inputted to a spectrum calculating means 1205, where a spectrum is calculated. A pseudo spectrum in a direction θ in MUSIC method when Rxx is used as a correlation matrix is obtained by formula 16. a(θ) is a complex steering vector (size K) in the direction θ. Superscript H means conjugate transposition.
                                          SPE            MUSIC                    ⁡                      (            θ            )                          =                  1                                                    a                ⁡                                  (                  θ                  )                                            H                        ⁢                          E              N                        ⁢                          E              N              H                        ⁢                          a              ⁡                              (                θ                )                                                                        (        16        )            
When θ is equal to the actual arrival direction, SPE (θ) becomes the infinite value. Therefore, a direction θ having a peak value in the calculation result of SPE becomes an estimated value of the arrival wave direction. Meanwhile, a pseudo spectrum in the direction θ when Ryy is used as a correlation matrix is obtained by formula 17. d(θ) is a real number steering vector sized K. QK is a unitary matrix sized K*K (refer to nonpatent document 1). Superscript T means transposition.
                                                                                          SPE                  UMUSIC                                ⁡                                  (                  θ                  )                                            =                              1                                                                            d                      ⁡                                              (                        θ                        )                                                              T                                    ⁢                                      E                    N                                    ⁢                                      E                    N                    T                                    ⁢                                      d                    ⁡                                          (                      θ                      )                                                                                                                                                              where                ⁢                                                                  ⁢                                  d                  ⁡                                      (                    θ                    )                                                              =                                                Q                  K                  T                                ⁢                                  a                  ⁡                                      (                    θ                    )                                                                                                          (        17        )            
As described above, to obtain the arrival direction, it is firstly necessary to calculate the spectrum over the all directions θ desired to be observed. After that, estimation is made so that the direction corresponding to a peak value of the spectrum is the estimated arrival direction. In the processing for estimating the arrival direction, the spectrum calculation amount is generally large. Therefore, in the past, several methods to reduce the spectrum calculation amount have been proposed. The following patent document 2 discloses a method of calculating the spectrum SPEMUSIC of the foregoing formula 16 by using FFT (Fast Fourier Transform). However, the method is not able to be used for calculating the spectrum SPEUMUSIC of the foregoing formula 17. Further, The following patent document 3 discloses a method in which the arrival direction is obtained with a low degree of precision by beam former method with the less calculation amount, and then the MUSIC spectrum is calculated only for the periphery thereof. In this case, it is necessary to calculate the spectrum by a plurality of methods, generally leading to complex processing. Further, the following patent document 4 discloses a method as follows. The method is used in the case that the antenna elements composing the array antenna are linearly arranged at equal intervals. The spectrum result in the positive (or negative) region is converted to the spectrum result in the negative (or positive) region, and thus the calculation amount of the spectrum SPEUMUSIC of the foregoing formula 17 is reduced by half. In this case, the calculation amount is only reduced by about half at maximum. Further, to improve the direction estimation precision, it is necessary to set short frequency division, leading to a further increased calculation amount.
Next, CAPON method will be described with illustration. The procedure until the correlation matrix calculation is similar to that of MUSIC method, and thus the description thereof will be omitted. The CAPON spectrum in the case of using the complex correlation matrix Rxx and the real number correlation matrix Ryy can be obtained by the following formulas 18 and 19 respectively. Superscript −1 represents an inverse matrix.
                                          SPE            CAPON                    ⁡                      (            θ            )                          =                  1                                                    a                ⁡                                  (                  θ                  )                                            H                        ⁢                          R              xx                              -                1                                      ⁢                          a              ⁡                              (                θ                )                                                                        (        18        )                                                      SPE            UCAPON                    ⁡                      (            θ            )                          =                  1                                                    d                ⁡                                  (                  θ                  )                                            T                        ⁢                          R              yy                              -                1                                      ⁢                          d              ⁡                              (                θ                )                                                                        (        19        )            
As a device to reduce the calculation amount of the CAPON spectrum, the following patent document 4 discloses a method in which the inverse matrix of the correlation matrix is once decomposed into an upper triangular matrix or a lower triangular matrix by using Choleski decomposition, and then the spectrum is calculated. However, in this method, for example, it is not possible to expect effects when the ratio of the Choleski decomposition calculation amount in relation to the whole spectrum calculation amount becomes large, for example, when there are different correlation matrices for each observed distance and the number of calculated direction in each spectrum is small. The flow from after the spectrum calculation the to arrival direction estimation is similar to that of MUSIC method.
Nonpatent document 1: “Adaptive signal processing by array antenna,” Nobuyoshi Kikuma, Science technology Co., 1998.
Nonpatent document 2: “Multiple Emitter Location and Signal Parameter Estimation,” R. O. Schmidt, IEEE Trans., AP-34, pp. 276-280 (1986).
Patent document 1: Japanese Patent Application Publication No. 11-344517, paragraph 0018 and Abstract.
Patent document 2: Japanese Patent Application Publication No. 2001-305202, paragraph 0033 and Abstract.
Patent document 3: Japanese Patent Application Publication No. 11-231033, paragraph 0019.
Patent document 4: Japanese Patent Application Publication No. 2002-243826, paragraph 0168.
As described above, to obtain the arrival direction, it is firstly necessary to calculate the spectrum over the all directions θ desired to be observed. The calculation amount therein is generally large. In the past, several methods to reduce the calculation amount have been proposed. However, the existing methods hereto proposed have the problems as follows. For example, one of the methods is not able to be applied to the case using unitary method. One of the methods makes the processing complicated. In one of the methods, the reduction effect is not sufficient, and in addition, to improve the direction estimation precision, it is necessary to set the short frequency division, leading to a further increased calculation amount.